After checking out about 8 of the most forum-recommended mass combat systems (in no order : War Machine, GURPS, Kingmaker, Heroes Of Battle, Conan, Die Men!, Green Ronin, Cry Havoc), I focused my attention on Kingmaker because it was by far the simplest system, using much of the existing system’s structure, with the fewest army “specs” (numbers), and melee rolls that are very similar to ordinary combat (d20+“to hit” bonus vs. AC, with a damage bonus if successful). It incorporates many tactical options into the attack, AC, and damage modifiers, thus allowing players to implement tactical choices easily. It is also in theory usable with any recent “d20”-based system.
As a computer programmer with decades of experience, I decided to simulate the Kingmaker mass combat system, to see how well things worked or didn’t.
First off, there are many variations on this system. I believe it was first introduced in Kingmaker, then modified for Ultimate Campaign, and it is now on the Pathfinder SRD (which added many more Special Abilities, and some other new features). First I analyzed the PF rules (without most their extras), then a Wikidot with yet some other changes. Regardless of the specific version you’re using, many of these results will be identical.
Keep in mind in all of the following that “CR” refers to the army’s CR, which varies by its size and the kind of creatures in it. So an army that is 3 CR smaller than another could have fewer soldiers, or soldiers with a smaller individual CR, or a little of both. But it could also have higher-CR troops, just very few of them, which is somewhat counter-intuitive.
In all simulations, I pitted two identical armies against each other from CR=1 to CR=20. The initial results were :
Everything was always significantly different for CR=1 to 5, so the following results ignore CR 1-5 battles. These are probably pretty uncommon anyway, requiring small numbers of low-CR creatures.
The average duration of a battle is about 6 rounds at the lowest CRs (6-7) to about 12 rounds at the highest (19-20).
There is always about a 5-10% chance that both armies are defeated (die, routed) on the same round. The lower the CR, the better the chances of a tie.
If the CRs differ by more than 3, the smaller CR army WILL lose. This does not account for all the other modifiers discussed below, which can make a significant difference.
Next I wanted to see how much each individual Strategy, Tactic, Resource, Special Ability, and Battlefield Condition modifier tipped the odds in favor of one army over the other (still with otherwise evenly matched armies). This assumes that one army uses the same single modifer thruout the entire battle, while the other army has no mods.
In general, each army has about a 46% chance of winning (with the remainder going to a tie). So if some modifier increases that army’s chance of winning to 56%, that’s listed as a “10% increase to winning”. Note that when the increase gets to be about 50% or more, that’s a guaranteed win!
First I found that the increases to winning that single bonuses to OM (attack bonus), DV (AC bonus), or DM (damage bonus) are :
Boosting the OM by +N gives a 10*N% increase to winning
Example : a +2 to OM increases the chance of winning by 20%
Boosting the DV by +N gives a 12*N% increase to winning
Boosting the DM by +N gives a 6*N% increase to winning
The above only applies for +1 to +3 bonuses. So a +1 bonus to one of these numbers does not correspond to a +5% increase in winning, and a +1 to OM does not improve your odds the same as a +1 to DM (for example).
Any "automatic win" condition can be converted into a "CR+" value, where the army WITHOUT the condition must be so many CR higher than the army WITH the condition to make it a fair fight. So if a condition is listed as “CR+3”, then to have a 50/50 chance of winning against a CR 10 army with that condition, an otherwise identical army (that is, using the same Strategy, Tactic, etc.) would need to be CR 13.
Conversely, each %increase in winning can be converted into a CR+ :
+21% (give or take) = +1 CR
+42% (give or take) = +2 CR
So a %increase in winning of about 19-24% (like OM+2 or DV+2) could be balanced by making the opposing army 1 CR higher, etc.
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TACTICS (N/A = Tactic could not be simulated easily)
Cautious Combat : –20% (has a smaller chance of winning)
Cavalry Experts : 20% vs. un-Mounted opponents
Defensive Wall : 16%
Dirty Fighters : N/A
Expert Flankers : –2%
False Retreat : N/A
Full Defense : 2%
Relentless Brutality : 2%
Siegebreaker : N/A, but essential for taking out siege engines
Sniper Support : 12% vs. un-Ranged opponents
Spellbreaker : see below
Standard : no change
Taunt : N/A
Withdraw : N/A
RECOMMENDATIONS :
1. Change or remove Expert Flankers, Full Defense, and Relentless Brutality – they give no advantage.
2. The only advantage Cautious Combat has is that it extends the duration of the battle, allowing time for help to arrive.
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RESOURCES
Healing Potions : 30% used once, 45% used twice (CR+2)
Improved/Magic Armor (+1, +2) : 12%, 24%
Improved/Magic Weapons (+1, +2) : 10%, 20%
Mounts : N/A
Ranged Weapons : N/A
Siege Engines : N/A
RECOMMENDATIONS :
The use of healing potions should be limited, as they increase the chances of winning by a large amount.
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SPECIAL ABILITIES
The initial Special Abilities from Kingmaker are listed, along with just a few of the MANY that PF added. Note that many of those added can counter various Battlefield Condition modifiers.
Breath Weapon : 14%
Construct/Plant/Undead/Mindless : N/A
Damage Reduction : 8% for 1 DR
Damage Reduction : 16% for 2 DR
Damage Reduction : 26% for 3 DR
Energy Drain : 41% (CR+2)
Fast Healing, Regeneration : +8% for 1 HP/rnd
Fast Healing, Regeneration : +16% for 2 HP/rnd
Fast Healing, Regeneration : +26% for 3 HP/rnd
Fear : N/A
Invisibility : 38% (CR+2)
Mobility : 10% vs. those without the situational advantage
Paralysis : 32%
Poison (also Bleed, Burn, Ability Damage or Drain) : 20% on average
Rock Throwing : 21%
Significant Defense : automatic win (CR +4)
Spell Resistance : see below
Spellcasting : 21% for max spell level = 1
Spellcasting : 38% for max spell level = 2
Spellcasting : automatic win for max spell level = 3 (CR+2)
Spellcasting : automatic win for max spell level = 4 (CR+3)
Spellcasting : automatic win for max spell level = 5 (CR+4)
RECOMMENDATIONS :
The “adding spellcasting to the army” rules are broken. See the next post for more details.
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BATTLEFIELD MODS
I did not check all the many weather conditions (fog, rain, sand, snow, wind) that Pathfinder added because they affect all armies equally, altho some of the new Special Abilities do negate them. And, some of them could not be simulated easily.
Advantageous Terrain : 24%
Ambush : N/A
Battlefield Advantage : 38%
Darkness : 45% vs. enemy who can’t see in darkness (CR +2)
Dim light : 10% vs. enemy who can’t see in dim light
Fortifications (+8 default) : automatic win (CR +3)
RECOMMENDATIONS :
1. Most of these provide tremendous advantages, and Darkness is a virtual win. The opposing side should look for Tactics and Strategies which would increase their OM mod to offset the large bonuses to DV that these provide. Or, the CR of the opposing side should be higher to compensate.
2. Note that having Fortifications is a virtual win by a large margin, and there’s no good way to counter it that I know of in the Pathfinder rules (other than having a much larger army), but see the “Wallsmasher” Tactic in the third post.
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TACTIC VS. COUNTER-TACTIC
Next, I tried giving one army one Tactic, and the other army the counter-tactic or not. The first number is the %increase in winning the Tactic gives to the first army, and the second number is the result when the opposing army has the given counter-tactic.
The only combination I could try with Pathfinder’s Tactics were for the spellcasters. See the third post for more combinations using its added Tactics.
Spellcaster(SL=1) vs. Spellbreaker : 21% --> –23% (the side with spellcasters loses more often!)
Spellcaster(SL=2) vs. Spellbreaker : 38% --> 0% (evenly matched battle)
Spellcaster(SL=3) vs. Spellbreaker : WIN --> 26%
Spellcaster(SL=4) vs. Spellbreaker : WIN --> 43%
Spellcaster(SL=5) vs. Spellbreaker : WIN --> WIN
RECOMMENDATIONS :
1. There is no existing Tactic that’s good against Cavalry Experts.
2. The “adding spells to armies” rules are broken – see the next post for more details
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STRATEGIES
Defensive : –45% (always loses)
Cautious : –26%
Standard : 0%
Aggressive : 15%
Reckless : 26%
The advantage to Defensive or Cautious is that they extend the duration of the battle, giving more time for help to arrive.
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STRATEGY VS. STRATEGY
Defensive vs. Defensive : 2%
Defensive vs. Cautious : –43% (LOSE)
Defensive vs. Standard : –45% (LOSE)
Defensive vs. Aggressive : –45% (LOSE)
Defensive vs. Reckless : –45% (LOSE)
Cautious vs. Defensive : 50% (WIN)
Cautious vs. Cautious : 2%
Cautious vs. Standard : –26%
Cautious vs. Aggressive : –35%
Cautious vs. Reckless : –39%
Standard vs. Defensive : 52% (WIN)
Standard vs. Cautious : 29%
Standard vs. Standard : 0%
Standard vs. Aggressive : –19%
Standard vs. Reckless : –30%
Aggressive vs. Defensive : 52% (WIN)
Aggressive vs. Cautious : 38%
Aggressive vs. Standard : 15%
Aggressive vs. Aggressive : –2%
Aggressive vs. Reckless : –6%, more ties
Reckless vs. Defensive : 53% (WIN)
Reckless vs. Cautious : 42% (WIN)
Reckless vs. Standard : 26%
Reckless vs. Aggressive : 7%, more ties
Reckless vs. Reckless : many more ties
Note that when both sides use the same Strategy, the change in winning is virtually zero (sanity check).
Any two Strategies more than 2 steps apart usually results in a win for the more aggressive strategy.
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TWO ARMIES VS. ONE ARMY
Finally, I tried pitting 1 large army against 2 smaller armies, again without any other modifiers.
One version of these rules claims that “two CR 9 armies should make for a relatively even battle, but so would a CR 9 army against three CR 6 armies”. And one of Paizo’s creative directors also implied that the CRs of the armies should combine by the regular CR rules. Following the CR rules for a 2 vs. 1 battle, the battle should be evenly matched if the two armies have a CR that is 2 less than the single army, but I found this was NOT true.
To produce an evenly matched battle, the simulation shows that the CRs must be :
CR1 : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
CR2 : - - 1 2 3 4 4 5 6 7 8 9 10 11 12 12 13 14 15 16
Diff : 1 1 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4
The “sweet spot” for 2 vs. 1 is that the CR of the 2 armies should be 3 less than the single army, across CR=7 to 15 (probably the most typical CRs). So the CR ratings of the armies do not combine as they should.
As a BTW, a single army always wins against two armies whose CRs are 5 or less than the single one’s CR. So a CR=15 army will always beat 2 armies whose CRs are 10 or less. Again, this is without any of the many modifiers, which can make a significant difference.
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SUMMARY
Please keep in mind that all of these tests assumed equal-CR armies, and are assuming you want a fair (50/50) fight. If you want to skew the fight slightly in favor of the players, make sure their OM/DV/damage bonuses are +1 to +3 above yours (that’s total, not each, and only if the CR’s are equal – if not, sorry, you’re on your own).
Also, I can usually only test the effect of one change at a time, and the number of ways Tactics can combine with Strategies is so large it cannot be accounted for. Not to mention that the number of Resources you can add to an army depends strongly on the situation. So more complicated simulations are just not practical, due to the number of combinations.
Finally, in any single battle, the roll of the dice is WAY more important than the average results shown here.
